A Landau theory for wetting on spherical and cylindrical substrates is studied. The substrate parameters are the radius ${r}_{1}$, the surface field ${h}_{1}$, and the surface-coupling enhancement g. The adsorbate is characterized by correlation length \ensuremath{\xi} and critical temperature ${T}_{c}$. The global phase diagrams reveal important features which were omitted in previous works. For T${T}_{c}$, the phase diagrams are obtained numerically and with use of analytic approximations. For T\ensuremath{\ge}${T}_{c}$, they are obtained exactly. For T${T}_{c}$, there are two distinct regimes of adsorption phase transitions: The regime \ensuremath{\xi}\ensuremath{\lesssim}${r}_{1}$\ensuremath{\le}\ensuremath{\infty} where the curvature of the substrate is small and the adsorbate is away from criticality, and the regime 0${r}_{1}$\ensuremath{\lesssim}\ensuremath{\xi} where the curvature is high and the adsorbate is near-critical. In the former regime, the phase transitions are referred to as ``surface'' transitions, and in the latter regime as ``point'' transitions (for spheres) and ``line'' transitions (for cylinders). The two regimes merge at a critical double point in the phase diagram. Beyond this point adsorption phase transitions can occur for arbitrary curvature and for all temperatures, including ${T}_{c}$. The wetting layer thicknesses behave as \ensuremath{\xi} ln(${r}_{1}$/\ensuremath{\xi}) for ${r}_{1}$\ensuremath{\gg}\ensuremath{\xi} and as \ensuremath{\xi} for ${r}_{1}$\ensuremath{\ll}\ensuremath{\xi}. The finite-size rounding of the phase transitions is discussed, and the experimental relevance of our findings is outlined.